Concepts/Formulas used:

Charge on Capacitor during Discharging (RC Circuit):

A capacitor of capacitance with charge C is being discharged through a resistor of resistance R. A switch S is also connected in series with the capacitor. The switch is initially open. At t=0, the switch is closed. The charge on the capacitor at any time t>0 is given by:

where and Q_i is the initial charge on the capacitor.

Note that the capacitor begins charging at t = 0.

Capacitance:

If two conductors have a potential difference V between the them and have charges Q and -Q respectively on them, then their capacitance is defined as

Let a capacitor of capacitance C be discharged through a resistor of resistance R. Switch S in attached is series and in initially open. It is closed at t = 0.

Charge is maximum when the capacitor is fully charged. Hence,

Now, we have at any time t>0,

We want to find t such that

Hence, we need 6.9 time constants.